6000 2000 2000 people

parameter estimates

##      true_param   mean se_mean    sd   2.5%    25%    50%    75%  97.5%
## bu11     -1.000 -0.982   0.009 0.100 -1.188 -1.045 -0.978 -0.914 -0.803
## bu12      0.500  0.482   0.004 0.057  0.377  0.443  0.479  0.517  0.600
## by1       1.000  1.080   0.001 0.044  0.994  1.050  1.080  1.110  1.170
## by2       0.500  0.461   0.000 0.028  0.406  0.442  0.461  0.480  0.515
## b00       0.000 -0.008   0.000 0.026 -0.059 -0.025 -0.008  0.010  0.044
## a11       0.290  0.406   0.004 0.064  0.290  0.362  0.403  0.447  0.541
## b0        0.367  0.358   0.000 0.037  0.286  0.333  0.359  0.383  0.429
## b11      -0.102 -0.151   0.002 0.037 -0.228 -0.175 -0.149 -0.126 -0.083
##          n_eff  Rhat
## bu11   134.410 1.040
## bu12   195.452 1.029
## by1   3030.023 1.001
## by2   4022.724 1.001
## b00  14374.736 1.000
## a11    234.496 1.025
## b0   14616.350 1.000
## b11    558.955 1.011

diagnostics

Gew

## [[1]]
## $z
##       b00        a1        b0        b1 
## -1.325567  2.044956  2.087751 -2.107862 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[2]]
## $z
##        b00         a1         b0         b1 
##  0.2058244  5.2693592 -0.9719592 -5.1046798 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[3]]
## $z
##         b00          a1          b0          b1 
## -0.35471730 -0.02685928 -0.09335141 -0.41333270 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[4]]
## $z
##        b00         a1         b0         b1 
## -0.8192404 -1.2368333  0.5773613  1.2029881 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"

Hei

## [[1]]
##     stest start      pvalue htest         mean   halfwidth
## b00     1     1 0.551879628     0 -0.007855843 0.000861323
## a1      1  1201 0.149916491     1  0.393233419 0.011512881
## b0      1     1 0.393124292     1  0.358808266 0.001219319
## b1      0    NA 0.008930648    NA           NA          NA
## attr(,"class")
## [1] "heidel.diag"
## 
## [[2]]
##     stest start     pvalue htest         mean    halfwidth
## b00     1     1 0.26309463     0 -0.007609394 0.0009366475
## a1      1   401 0.09333343     1  0.397689073 0.0129376752
## b0      1     1 0.67322360     1  0.358837337 0.0012740540
## b1      1   801 0.40929085     1 -0.146488703 0.0043074332
## attr(,"class")
## [1] "heidel.diag"
## 
## [[3]]
##     stest start    pvalue htest         mean    halfwidth
## b00     1     1 0.7332151     0 -0.007581359 0.0007600748
## a1      1     1 0.2151050     1  0.417046097 0.0113723233
## b0      1     1 0.4324584     1  0.357603897 0.0011075361
## b1      1     1 0.1565668     1 -0.154305867 0.0038818496
## attr(,"class")
## [1] "heidel.diag"
## 
## [[4]]
##     stest start    pvalue htest         mean    halfwidth
## b00     1     1 0.1719269     0 -0.007587441 0.0008185767
## a1      1     1 0.7312229     1  0.397375858 0.0117226317
## b0      1     1 0.5779112     1  0.357912749 0.0011924530
## b1      1     1 0.7165879     1 -0.147664502 0.0053830601
## attr(,"class")
## [1] "heidel.diag"

Gel

## $psrf
##     Point est. Upper C.I.
## b00   1.000022   1.000207
## a1    1.019958   1.058527
## b0    1.000178   1.000664
## b1    1.007320   1.021281
## 
## $mpsrf
## [1] 1.019161
## 
## attr(,"class")
## [1] "gelman.diag"

plots

Traceplots

Autoregression

Pair plots

6000 2000 1000 people

parameter estimates

##      true_param   mean se_mean    sd   2.5%    25%    50%    75% 97.5%
## bu11     -1.000 -0.558   0.484 0.690 -1.163 -0.993 -0.901 -0.363 0.687
## bu12      0.500  0.297   0.259 0.370 -0.382  0.169  0.475  0.534 0.643
## by1       1.000  0.979   0.001 0.066  0.851  0.935  0.979  1.025 1.107
## by2       0.500  0.459   0.001 0.042  0.376  0.431  0.459  0.488 0.542
## b00       0.000  0.000   0.000 0.037 -0.072 -0.025  0.000  0.025 0.072
## a11       0.202  0.074   0.163 0.245 -0.473 -0.017  0.169  0.238 0.360
## b0        0.348  0.318   0.000 0.053  0.216  0.283  0.318  0.354 0.422
## b11      -0.158 -0.078   0.160 0.233 -0.318 -0.230 -0.182 -0.011 0.412
##          n_eff  Rhat
## bu11     2.033 7.700
## bu12     2.047 6.371
## by1   5449.988 1.001
## by2   6990.670 1.001
## b00  21749.650 1.000
## a11      2.261 2.819
## b0   21487.991 1.000
## b11      2.124 3.931

diagnostics

Gew

## [[1]]
## $z
##          b00           a1           b0           b1 
## -0.003103772 -0.450802066 -1.023556991  0.549202952 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[2]]
## $z
##       b00        a1        b0        b1 
## -1.762320  1.405193  1.576799 -1.533944 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[3]]
## $z
##        b00         a1         b0         b1 
##  1.3552276  2.4556738  0.1350465 -2.7128232 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[4]]
## $z
##        b00         a1         b0         b1 
## -0.8668600  0.3589309 -0.8772519 -0.2431312 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"

Hei

## [[1]]
##     stest start    pvalue htest          mean   halfwidth
## b00     1     1 0.9458590     0  0.0002899092 0.001008130
## a1      1     1 0.6861457     1  0.2098877684 0.006503588
## b0      1     1 0.5177893     1  0.3185764258 0.001403192
## b1      1     1 0.6511787     1 -0.2112186275 0.006311526
## attr(,"class")
## [1] "heidel.diag"
## 
## [[2]]
##     stest start     pvalue htest          mean    halfwidth
## b00     1     1 0.55144075     0  0.0007760678 0.0009782975
## a1      1     1 0.06535033     1  0.2057958966 0.0048620750
## b0      1     1 0.35850554     1  0.3175806693 0.0014631214
## b1      1     1 0.39867569     1 -0.2064221377 0.0049855042
## attr(,"class")
## [1] "heidel.diag"
## 
## [[3]]
##     stest start     pvalue htest          mean    halfwidth
## b00     1     1 0.12704896     0  0.0003885021 0.0009192883
## a1      1   401 0.14857474     1  0.1976815291 0.0045577804
## b0      1     1 0.94004220     1  0.3186613804 0.0012517670
## b1      1     1 0.07015147     1 -0.2042649729 0.0054779955
## attr(,"class")
## [1] "heidel.diag"
## 
## [[4]]
##     stest start     pvalue htest          mean   halfwidth
## b00     1     1 0.29321385     0  0.0001381831 0.001007809
## a1      1     1 0.29799265     1 -0.3191806892 0.008312927
## b0      1     1 0.08066465     1  0.3186630454 0.001424145
## b1      1     1 0.05121997     1  0.3105814922 0.004769708
## attr(,"class")
## [1] "heidel.diag"

Gel

## $psrf
##     Point est. Upper C.I.
## b00  0.9999226   1.000082
## a1   4.0045901   7.227404
## b0   1.0000092   1.000357
## b1   5.7002805  10.321612
## 
## $mpsrf
## [1] 4.700347
## 
## attr(,"class")
## [1] "gelman.diag"

plots

Traceplots

Autoregression

Pair plots

10000 3000 1000 people

parameter estimates

##      true_param   mean se_mean    sd   2.5%    25%    50%    75%  97.5%
## bu11     -1.000 -0.856   0.004 0.098 -1.062 -0.919 -0.851 -0.788 -0.681
## bu12      0.500  0.381   0.002 0.057  0.279  0.341  0.378  0.416  0.501
## by1       1.000  1.050   0.001 0.067  0.918  1.006  1.050  1.095  1.182
## by2       0.500  0.519   0.000 0.037  0.446  0.494  0.519  0.544  0.593
## b00       0.000 -0.019   0.000 0.035 -0.088 -0.043 -0.020  0.004  0.049
## a11       0.120  0.236   0.002 0.090  0.065  0.175  0.233  0.294  0.421
## b0        0.331  0.291   0.000 0.051  0.192  0.256  0.290  0.325  0.391
## b11      -0.157 -0.261   0.001 0.061 -0.388 -0.300 -0.258 -0.219 -0.149
##          n_eff  Rhat
## bu11   478.604 1.006
## bu12   776.059 1.004
## by1   8554.603 1.000
## by2  11287.826 1.000
## b00  36397.075 1.000
## a11   3137.879 1.002
## b0   36204.934 1.000
## b11   1710.431 1.003

diagnostics

Gew

## [[1]]
## $z
##        b00         a1         b0         b1 
##  0.3307758 -0.5542532  1.3853679  0.5949188 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[2]]
## $z
##        b00         a1         b0         b1 
##  0.5240336  3.5672610 -1.8686155 -3.7717234 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[3]]
## $z
##        b00         a1         b0         b1 
## -0.2649822  0.6664967  0.3499358 -0.3841606 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"
## 
## [[4]]
## $z
##        b00         a1         b0         b1 
## -0.6410726  2.8343666  1.2631906 -2.1522449 
## 
## $frac
## [1] 0.1 0.5
## 
## attr(,"class")
## [1] "geweke.diag"

Hei

## [[1]]
##     stest start     pvalue htest       mean    halfwidth
## b00     1     1 0.61892803     1 -0.0194903 0.0006663618
## a1      1  1401 0.63735736     1  0.2368613 0.0056681550
## b0      1     1 0.72815414     1  0.2902114 0.0009461220
## b1      1     1 0.08374458     1 -0.2586166 0.0042275413
## attr(,"class")
## [1] "heidel.diag"
## 
## [[2]]
##     stest start    pvalue htest        mean    halfwidth
## b00     1     1 0.5867706     1 -0.01916182 0.0007553557
## a1      1  2801 0.2947750     1  0.22758790 0.0055746177
## b0      1     1 0.1079319     1  0.29022477 0.0010903868
## b1      1  1401 0.1680431     1 -0.25856091 0.0060207748
## attr(,"class")
## [1] "heidel.diag"
## 
## [[3]]
##     stest start    pvalue htest        mean    halfwidth
## b00     1     1 0.7257837     1 -0.01918389 0.0007304293
## a1      1     1 0.4241069     1  0.23622225 0.0058337377
## b0      1     1 0.2484061     1  0.29052083 0.0010866741
## b1      1     1 0.3094243     1 -0.26040524 0.0050758854
## attr(,"class")
## [1] "heidel.diag"
## 
## [[4]]
##     stest start     pvalue htest        mean    halfwidth
## b00     1  2801 0.09942063     1 -0.01939618 0.0009126121
## a1      1     1 0.06253777     1  0.23511156 0.0048724445
## b0      0    NA 0.01699592    NA          NA           NA
## b1      1     1 0.10439261     1 -0.26051430 0.0039407710
## attr(,"class")
## [1] "heidel.diag"

Gel

## $psrf
##     Point est. Upper C.I.
## b00   1.000207   1.000386
## a1    1.000644   1.002158
## b0    1.000043   1.000048
## b1    1.000383   1.001290
## 
## $mpsrf
## [1] 1.000651
## 
## attr(,"class")
## [1] "gelman.diag"

plots

Traceplots

Autoregression

Pair plots